Dependence Models for Actuarial Data.

当我们将模型匹配到数据时，我们通常感兴趣的是以尽可能好的方式表示数据，因此找到一个适合整个数据集的模型。然而，当重点关注于捕捉极端事件的行为时--例如洪水或巨额经济损失--这些模型就不会有很好的表现。作为解决方案，可以应用极值方法来仅对尾部的数据进行建模。但是，非极端数据也令人感兴趣的情况又如何呢？当现有数据涉及单一变量时--例如，对特定地点的降雨量分布进行建模--现有的统计方法旨在准确地对分布的主体(即非极端数据)和分布的尾部(即极端事件)进行建模。然而，当我们有一个以上的变量时--例如，当精算师有兴趣对负债之间的相关性进行建模以了解风险敞口时--情况就更加复杂，对于极端情况和身体都涉及的情况，人们所做的工作很少。该项目旨在通过调查和开发相关性模型来填补这一空白，该模型允许适当地考虑尾部，以及准确地对数据正文进行建模。

When we fit a model to data, we are usually interested in representing the data the best way possible, and therefore in finding a model that fits the entire data set well. However, when the focus is on capturing the behaviour of extreme events - such as floods or large financial losses, for example - these models won't perform well. As a solution, extreme value methods can be applied to model only the data in the tail. But what about the situation where the non-extreme data are also of interest? When the data available concerns a single variable - for example, the modelling of the rainfall distribution at a particular location - there are statistical methods available that aim to accurately model the body of the distribution (i.e., data that aren't extreme) and the tail of the distribution (i.e., extreme events). However, when we have more than one variable - for example when an actuary is interested in modelling the dependence between liabilities in order to understand the exposure to risk - the situation is more complex, and sparse work has been done concerning the case where both extremes and the body are of interest. This project aims to fill this gap by investigating and developing dependence models which allow the tails to be considered appropriately, as well as accurately modelling the body of the data.In partnership with University College Dublin.